Avoiding Common Mistakes

Watch out for these errors:

$1.$ Confusing $/$ and $\bmod$. Division gives the quotient, modulo gives the remainder. Both are needed for different purposes.

$2.$ Forgetting parentheses with mixed operations. $a + b \bmod c$ is not the same as $(a + b) \bmod c$.

$3.$ Ignoring negative numbers. Modulo behavior with negatives varies by language. Use $(a \bmod m + m) \bmod m$ for safety.

$4.$ Not applying modulo in intermediate steps. Large multiplications overflow if you don't reduce before the next operation.